Sampling distribution

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In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, a sampling distribution or finite-sample distribution is the <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> of a given <a href="/facts/Random_sample/URCwKNge">random-sample</a>-based <a href="/facts/Statistic/av21WaMK">statistic</a>. For an arbitrarily large number of samples where each sample, involving multiple observations (data points), is separately used to compute one value of a statistic (for example, the <a href="/facts/Sample_mean/Ah8VVVDT">sample mean</a> or sample <a href="/facts/Variance/ULBJKXD1">variance</a>) per sample, the sampling distribution is the probability distribution of the values that the statistic takes on. In many contexts, only one sample (i.e., a set of observations) is observed, but the sampling distribution can be found theoretically.
</p><p>Sampling distributions are important in statistics because they provide a major simplification en route to <a href="/facts/Statistical_inference/sJLjubxm">statistical inference</a>. More specifically, they allow analytical considerations to be based on the probability distribution of a statistic, rather than on the <a href="/facts/Joint_probability_distribution/klX2ksGY">joint probability distribution</a> of all the individual sample values.
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Sampling distribution open-in-new

Sampling distribution